§ DICTIONARY · PHENOMENON

Frame Dragging

A rotating mass twists the spacetime around it, forcing nearby objects to co-rotate.

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Definition

Frame dragging is the prediction of general relativity that a rotating mass does not merely curve the spacetime around it but also sets it spinning. An object that falls freely toward a rotating body with no angular momentum of its own nonetheless acquires an angular velocity, measured by a distant observer, in the same direction as the rotation. The local inertial frames — the frames in which the laws of physics take their special-relativistic form — are themselves dragged around the spinning source.

The effect was first derived in 1918 by Josef Lense and Hans Thirring as a weak-field consequence of Einstein's equations, and is often called the Lense–Thirring effect in that regime. Far from the source the dragging angular velocity falls off as 1/r³, making it minuscule for ordinary bodies: around the spinning Earth it amounts to a precession of about 37 milliarcseconds per year, a value confirmed by the Gravity Probe B satellite in 2011 and by laser-ranging to the LAGEOS satellites.

Near a rotating black hole the effect becomes extreme. Inside the static limit of the Kerr metric, frame dragging is so strong that no object can remain at a fixed angular position no matter how powerfully it thrusts — co-rotation becomes mandatory. At the event horizon the dragging angular velocity reaches a fixed value Ω_H, and everything that crosses the horizon rotates with it exactly. Frame dragging is the physical origin of the ergosphere and of the energy that the Penrose and Blandford–Znajek processes extract from a spinning black hole.

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History

Predicted by Lense and Thirring in 1918 from Einstein's 1915 field equations; the strong-field version emerged from Roy Kerr's 1963 rotating-black-hole solution; directly measured around the Earth by Gravity Probe B (2011) and satellite laser ranging.

Frame Dragging — physics